Scott Olsen, the Iraq war veteran who suffered serious head injuries after being hit by a projectile fired by police during the Occupy Oakland protests, has woken up and is lucid as he awaits surgery, hospital officials and family members have said.

Olsen, a 24-year-old former US Marine, was struck in the head during anti-Wall Street protests on Tuesday night. He has been upgraded from critical to fair condition.

Olsen "responded with a very large smile" to a visit from his parents, Highland General hospital spokesman Warren Lyons said. "He's able to understand what's going on. He's able to write and hear but has a little difficulty with his speech," Lyons said.

Doctors had not operated on Olsen yet and were waiting to see if swelling in his brain eased, Lyons said.

Olsen's aunt, Kathy Pacconi, told Reuters in an email that her nephew was showing signs of improvement.

Olsen, 24, has become a figurehead of the Occupy Wall Street movement and Oakland organisers have said they will stage a general strike over what a spokeswoman called the "brutal and vicious" treatment of protesters, including the former Marine.

Oakland's police chief, Howard Jordan, has promised a vigorous investigation into the incident which has provoked heavy criticism across the US, sparking solidarity marches in dozens of Occupy camps in the country.

This week's violent clashes with police in Oakland appear to have re-energised the Occupy movement in America, creating political liabilities for civic leaders across the United States, who had seemed poised to follow Oakland's lead and, in some cases, issued orders to clear the streets.

The White House said yesterday that Barack Obama understood the frustration of the Occupy Wall Street protesters but stressed the need to uphold the law.

White House spokesman Jay Carney, responding to reporters' questions about the Oakland violence, said he had not discussed protests in specifiic cities with the president, only the protests in general.

Obama has tried to maintain a balancing act as the protests have grown, leaning towards support while avoiding a full embrace of the movement. But it would be a huge step for the president to go on to criticise any police force.

Carney said the president could sympathised with the frustration over the role of Wall Street writ large in the worst recession since the Great Depression. There was a long and noble expression of free expression in the US, he said. But, as to the violence, he said the federal government obviously insisted that everyone behave in a lawful manner even as they expressed their frustration.

The Oakland protesters were back in force on Wednesday night, 24 hours after they were supposed to be gone for good, demanding the resignation of the city's mayor.

This time the police did nothing except circle around the demonstrators and discourage them from jumping on to an overhead freeway. More than 1000 protesters kept marching through the city streets until long after midnight, shouting an occasional "shame on you" at motorcycle cops and taking care to pick up their own litter. They even picked up pieces of a fence they had earlier pulled down and stacked them in neat piles around Frank Ogawa Plaza, in front of City Hall.

Oakland Mayor Jean Quan, herself a veteran of street protests from Berkeley in the 1960s to a public demonstration against police brutality in Oakland just lastyear, is facing demands for her recall or resignation. "Mayor Quan, you did more damage to Oakland in one evening than Occupy Oakland did in two weeks," one hastily scrawled slogan left near the entrance to her offices read.

In a news conference, Quan sought to distance herself from the police action, saying she was away in Washington at the time and had not expected it to unfold the way it did. "I only asked the chief to do one thing: to do it when it was the safest for both the police and the demonstrators," she said.

Her interim police chief, Howard Jordan, was similarly defensive when he spoke to reporters, denying that his men had used rubber bullets or flash-bang grenades, as some protesters alleged and adding: "It's unfortunate it happened. I wish that it didn't happen. Our goal, obviously, isn't to cause injury to anyone."